Using a bézier curve to raise/lower height of vertices?
You can, but you will have to use a workaround.



The principle is using a Vertex Weight Proximity modifier to influence displacement strength.

Issue is unfortunately you can't really use a bezier curve object directly, so you will have to use a mesh object with an Array modifier plus a Curve modifier to affect the displacement.

Just array to any mesh (possibly a simple cylinder) and add an Array modifier set to Fit Curve. Then add a Curve modifier on top of it, point it to the same bezier curve as described here.



On your (soon to be) deformed mesh create a vertex group and add all vertex to it. Then add a Vertex Weight Proximity modifier set to control that same vertex group in Distance to Geometry > Face mode.



Now add a displace modifier influenced by the above vertex group as described here, adjust values and distances as necessary.